多次元尺度構成法(MDS: Multi-Dimensional Scaling)

In [1]:

    

%matplotlib inline
import numpy as np
import pandas as pd
from sklearn.manifold import MDS
import matplotlib.pyplot as plt


    

In [2]:

    

# データの読み込み
data = pd.read_csv("data/tab71.csv", header=None)
labels = ["Urawa", "Chiba", "Tokyo", "Yokohama", "Hachiouji"]
data.head()


    

    
Out[2]:






  

    

      

      
0
      
1
      
2
      
3
      
4
    
  
  

    

      
0
      
0
      
49
      
22
      
44
      
37
    
    

      
1
      
49
      
0
      
34
      
47
      
71
    
    

      
2
      
22
      
34
      
0
      
27
      
39
    
    

      
3
      
44
      
47
      
27
      
0
      
33
    
    

      
4
      
37
      
71
      
39
      
33
      
0
    
  

In [3]:

    

# 古典的MDS
mds = MDS(2, dissimilarity="precomputed")
result = mds.fit_transform(data)
pd.DataFrame(result, index=labels)


    

    
Out[3]:






  

    

      

      
0
      
1
    
  
  

    

      
Urawa
      
12.950357
      
19.164610
    
    

      
Chiba
      
24.287706
      
-29.301523
    
    

      
Tokyo
      
6.244494
      
-1.289034
    
    

      
Yokohama
      
-19.041379
      
-10.677186
    
    

      
Hachiouji
      
-24.441177
      
22.103133
    
  

In [4]:

    

# プロット
plt.scatter(result[:, 0], result[:, 1])
for i in range(result.shape[0]):
    plt.text(result[:, 0][i], result[:, 1][i], labels[i], fontsize=12)
plt.title("MDS")


    

    
Out[4]:





<matplotlib.text.Text at 0x10926c650>